The increasingly popular and widespread mobile devices frequently include so-called nine-axis sensors which consist of a 3-axis (3-D) gyroscope, a 3-axis (3-D) accelerometer and a 3-axis (3-D) magnetometer. The 3-D gyroscope measures angular velocities. The 3-D accelerometer measures linear acceleration. The 3-D magnetometer measures a local magnetic field vector (or a deviation thereof). In spite of their popularity, the foreseeable capabilities of these nine-axis sensors are not fully exploited due to the difficulty of calibrating and removing undesirable effects from the magnetometer measurements on one hand, and the practical impossibility to make a reliable estimate of the yaw angle using only the gyroscopes and the accelerometer.
A rigid body's (i.e., by rigid body designating any device to which the magnetometer and motion sensors are attached) 3-D angular position with respect to an Earth-fixed gravitational orthogonal reference system is uniquely defined. When a magnetometer and an accelerometer are used, it is convenient to define the gravitational reference system as having the positive Z-axis along gravity, the positive X-axis pointing to magnetic North and the positive Y-axis pointing East. The accelerometer senses gravity defining the z-axis, and the magnetometer measurement is used to infer the magnetic North based on the Earth's magnetic field (noting here that it is known that the angle between the Earth's magnetic field and gravity is may be different from 90°). This manner of defining the axis of a gravitational reference system is not intended to be limiting. Other definitions of an orthogonal right-hand reference system may be derived based on the two known directions, gravity and the magnetic North.
Based on Euler's theorem, the body reference system and the gravitational reference system (as two orthogonal right-hand coordinate systems) can be related by a sequence of rotations (not more than three) about coordinate axes, where successive rotations are about different axis. A sequence of such rotations is known as an Euler angle-axis sequence. Such a reference rotation sequence is illustrated in FIG. 2. The angles of these rotations are angular positions of the device in the gravitational reference system.
A 3-D magnetometer measures a 3-D magnetic field representing an overlap of a 3-D static magnetic field (e.g., Earth's magnetic field), hard- and soft-iron effects, and a 3-D dynamic near field due to external time dependent electro-magnetic fields. The measured magnetic field depends on the actual orientation of the magnetometer. If the hard-iron effects, soft-iron effects and dynamic near fields were zero, the locus of the measured magnetic field (as the magnetometer is oriented in different directions) would be a sphere of radius equal to the magnitude of the Earth's magnetic field. The non-zero hard- and soft-iron effects render the locus of the measured magnetic field to be an ellipsoid offset from origin.
Hard-iron effect is produced by materials that exhibit a constant magnetic field with respect to the magnetometer's body frame overlapping the Earth's magnetic field, thereby generating constant offsets of the components of the measured magnetic field. As long as the orientation and position of the sources of magnetic field resulting in the hard-iron effects relative to the magnetometer is not changing, the corresponding offsets are also constant.
Unlike the hard-iron effect that yields a constant magnetic field in the magnetometer's body frame, the soft-iron effect is the result of material that influences, or distorts, a magnetic field (such as, iron and nickel), but does not necessarily generate a magnetic field itself. Therefore, the soft-iron effect is a distortion of the measured field depending upon the location and characteristics of the material causing the effect relative to the magnetometer and to the Earth's magnetic field. Thus, soft-iron effects cannot be compensated with simple offsets, requiring a more complicated procedure.
Conventional methods (e.g., J. F. Vasconcelos et al., A Geometric Approach to Strapdown Magnetometer Calibration in Sensor Frame, Proceeding of IFAC Workshop on Navigation, Guidance, and Control of Underwater Vehicles (NGCUV), Killaloe, Ireland, Volume 2, 2008, and R. Alonso and M. D. Shuster. Complete linear attitude-independent magnetometer calibration, The Journal of the Astronautical Sciences, 50(4):477-490, October-December 2002) use nonlinear least square fit techniques to determine the attitude-independent parameters. These methods may diverge or converge to a local minimum instead of a global minimum issue, require iterations and two steps to determine a solution.
Another known method (D. Gebre-Egziabher et al., Calibration of Strapdown Magnetometers in Magnetic Field Domain. ASCE Journal of Aerospace Engineering, 19(2):1-16, April 2006) determines some of the attitude-independent parameters analytically but yields an incomplete solution which does not account for skew, and, therefore, determining only 6 of the total 9 parameters based on the assumption that the skew is zero.
Therefore, it would be desirable to provide devices, systems and methods that enable real-time reliable use of a magnetometer together with other motion sensors attached to a device for determining orientation of the device (i.e., angular positions including a yaw angle), while avoiding the afore-described problems and drawbacks.